Teichmüller spaces and pseudo-Anosov homeomorphism (Part 1)

Appears in collection : Summer School 2018 - Teichmüller dynamics, mapping class groups and applications.

I will start by describing the Teichmuller space of a surface of finite type from the perspective of both hyperbolic and complex structures and the action of the mapping class group on it. Then I will describe Thurston's compactification of Teichmuller space, and state his classification theorem. After that, I will focus on pseudo-Anosov homeomorphisms, describe a little bit about their dynamics, and discuss the geometry/dynamics of the associated mapping tori.